This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (excluding yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.



**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species. 


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

##   [1] "beta2_pH"       "re_pelagic"     "beta1_pH"       "beta0_pH"      
##   [5] "mu_beta2_pH"    "re_pH"          "beta3_pH"       "Rb_ay"         
##   [9] "Rb_ay_mort"     "Rp_ay"          "Rp_ay_mort"     "Rb_ayu"        
##  [13] "Rb_ayu_mort"    "Rp_ayu"         "Rp_ayu_mort"    "R_ay"          
##  [17] "R_ayu"          "p_pelagic"      "Rp_ayg"         "Rp_ayg_mort"   
##  [21] "R_ayg"          "Rb_ayg"         "Rb_ayg_mort"    "Ro_ayu"        
##  [25] "Ro_ay"          "Bb_ayg"         "Tb_ayg"         "Tp_ayg"        
##  [29] "Bb_ay"          "Tb_ay"          "Tp_ay"          "Hy_ayu"        
##  [33] "Ty_ayu"         "Hy_ay"          "Ty_ay"          "Rdnye_ayu"     
##  [37] "Rdnye_ayu_mort" "By_ayu"         "By_ay"          "Ry_ayg"        
##  [41] "Ry_ayg_mort"    "Ry_ayu"         "Ry_ayu_mort"    "Rdnye_ay"      
##  [45] "Rdnye_ay_mort"  "pH"             "Tb_ayu"         "Hp_ay"         
##  [49] "Tp_ayu"         "Hb_ay"          "Bb_ayu"         "Ro_ayg"        
##  [53] "Ry_ay"          "Ry_ay_mort"     "Ho_ayu"         "Tdnye_ayu"     
##  [57] "mu3_wt"         "Bdnye_ayu"      "Rd_ay"          "Rs_ayu"        
##  [61] "Rs_ayu_mort"    "Ho_ay"          "Hb_ayg"         "Hp_ayg"        
##  [65] "Rd_ayu"         "Bp_ay"          "Bp_ayg"         "tau_beta1_pH"  
##  [69] "Rd_ayg"         "Hd_ay"          "Rdnye_ayg"      "Rdnye_ayg_mort"
##  [73] "tau_beta4_pH"   "Rs_ay"          "Rs_ay_mort"     "pDSR_YE_ay"    
##  [77] "Bs_ayu"         "Tdnye_ay"       "Bdnye_ay"       "Hp_ayu"        
##  [81] "p_dsr"          "re_dsr"         "sd3_wt"         "Hb_ayu"        
##  [85] "Ts_ayu"         "Ho_ayg"         "By_ayg"         "tau_beta0_pH"  
##  [89] "Ty_ayg"         "tau_beta2_pH"   "Hd_ayg"         "Rs_ayg"        
##  [93] "Rs_ayg_mort"    "p_yellow"       "pDSR_YE_ayu"    "pDSR_YE_ayg"   
##  [97] "H_ayu"          "Hy_ayg"         "H_ay"           "H_ayg"         
## [101] "Bp_ayu"
Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pelagic 4 1.607778
beta1_pelagic 6 1.520791
beta2_pH 7 1.438175
beta3_yellow 1 1.349932
beta1_yellow 6 1.327451
beta0_yellow 4 1.316115
beta1_pH 7 1.288583
parameter n badRhat_avg
beta0_pH 4 1.235325
beta2_pelagic 5 1.229667
beta3_pelagic 4 1.208330
beta3_pH 5 1.183367
beta2_yellow 4 1.170837
tau_beta0_pH 1 1.144732
Table 2. Summary of unconverged major parameters by area
Parameter CI NG PWSI PWSO BSAI SOKO2SAP WKMA afognak eastside northeast CSEO EWYKT NSEI NSEO SSEI SSEO
beta0_pH 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0
beta0_pH 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0
beta1_pH 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1
beta1_pH 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1
beta2_pH 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1
beta2_pH 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1
beta3_pH 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0
beta3_pH 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0
Bp_ay 0 0 0 0 0 0 0 0 0 0 18 0 0 1 0 0
Bp_ayg 0 0 0 0 0 0 0 0 0 0 14 2 0 1 0 0
Bp_ayu 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
H_ay 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
H_ayg 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
H_ayu 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
Hb_ay 0 0 0 0 1 0 0 0 0 0 19 0 0 0 0 1
Hb_ayg 0 0 0 0 1 0 0 0 0 0 15 0 0 0 0 0
Hb_ayu 0 0 0 0 1 0 0 0 0 0 7 0 0 0 0 1
Hd_ay 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0
Hd_ayg 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0
Ho_ay 0 0 0 0 3 1 0 0 0 0 2 0 0 0 0 0
Ho_ayg 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
Ho_ayu 0 0 0 0 3 1 0 1 1 0 0 0 0 0 0 0
Hp_ay 0 0 0 0 1 0 0 0 0 0 19 0 0 0 0 1
Hp_ayg 0 0 0 0 1 0 0 0 0 0 15 0 0 0 0 0
Hp_ayu 0 0 0 0 1 0 0 0 0 0 7 0 0 0 0 1
Hy_ay 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
Hy_ayg 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
Hy_ayu 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0
mu_beta2_pH 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
p_dsr 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
p_pelagic 0 0 0 20 0 0 0 0 0 0 41 0 0 0 0 0
p_yellow 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
pDSR_YE_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
pDSR_YE_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
pDSR_YE_ayu 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
pH 0 17 0 0 0 6 1 0 0 0 0 0 0 0 0 0
R_ay 5 13 5 5 4 11 9 7 7 9 0 6 0 4 0 2
R_ayg 6 13 5 6 5 10 9 7 7 10 0 7 0 4 0 3
R_ayu 1 11 1 1 4 11 1 2 1 5 0 1 0 0 0 0
Rb_ay 4 13 5 6 4 11 10 7 7 9 0 6 0 5 0 2
Rb_ay_mort 4 13 4 7 4 11 10 7 7 9 0 6 0 5 0 2
Rb_ayg 4 13 5 7 4 10 9 7 7 9 0 7 0 4 0 3
Rb_ayg_mort 4 13 5 7 4 10 9 7 7 9 0 7 0 4 0 3
Rb_ayu 2 13 2 3 4 11 4 3 1 4 0 1 0 3 0 0
Rb_ayu_mort 2 13 2 3 4 11 4 3 1 4 0 1 0 3 0 0
Rd_ay 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1
Rd_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rd_ayu 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2
Rdnye_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rdnye_ay_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rdnye_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
Rdnye_ayg_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
Rdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 4
Rdnye_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 4
re_pelagic 0 0 0 1 0 0 0 0 0 0 26 0 0 2 0 6
re_pH 0 12 0 0 0 0 6 7 0 0 0 0 0 0 0 11
Ro_ay 1 0 0 1 12 23 1 3 1 1 0 0 0 0 0 1
Ro_ayg 1 0 0 0 2 0 0 0 1 0 0 0 0 0 0 2
Ro_ayu 1 0 0 2 12 24 1 3 4 2 0 1 0 0 0 2
Rp_ay 7 13 5 6 4 11 10 7 7 9 0 6 0 5 0 2
Rp_ay_mort 6 13 4 7 4 11 10 7 7 9 0 6 0 5 0 2
Rp_ayg 6 13 5 7 5 10 9 7 8 10 0 7 0 4 0 3
Rp_ayg_mort 6 13 5 7 5 10 9 7 8 10 0 7 0 4 0 3
Rp_ayu 2 13 1 3 4 11 4 2 1 5 0 1 0 3 0 0
Rp_ayu_mort 2 13 1 3 4 11 4 2 1 5 0 1 0 3 0 0
Rs_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rs_ay_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rs_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rs_ayg_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rs_ayu 0 0 0 0 0 0 0 0 0 0 1 5 0 0 0 3
Rs_ayu_mort 0 0 0 0 0 0 0 0 0 0 1 5 0 0 0 3
Ry_ay 0 0 0 1 7 4 0 0 1 0 1 0 0 0 0 1
Ry_ay_mort 0 0 0 1 7 4 0 0 1 0 1 0 0 0 0 1
Ry_ayg 1 0 0 0 1 2 1 2 0 0 0 0 0 0 0 1
Ry_ayg_mort 1 0 0 0 1 2 1 2 0 0 0 0 0 0 0 1
Ry_ayu 0 0 0 1 8 4 0 0 1 0 2 0 0 0 0 2
Ry_ayu_mort 0 0 0 1 8 4 0 0 1 0 2 0 0 0 0 2
tau_beta0_pH 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta1_pH 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta2_pH 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta4_pH 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Tp_ay 0 0 0 0 1 6 3 2 2 0 18 1 0 1 0 0
Tp_ayg 0 0 0 0 0 3 3 3 2 3 15 2 0 1 0 0
Tp_ayu 0 0 0 0 3 6 1 2 0 0 2 0 0 0 0 0
beta0_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1
beta0_yellow 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1
beta1_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1
beta1_yellow 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1
beta2_pelagic 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1
beta2_yellow 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1
beta3_pelagic 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0
beta3_yellow 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.127 0.070 -0.258 -0.129 0.019
mu_bc_H[2] -0.102 0.047 -0.183 -0.106 0.001
mu_bc_H[3] -0.431 0.072 -0.571 -0.432 -0.288
mu_bc_H[4] -1.000 0.195 -1.404 -0.997 -0.622
mu_bc_H[5] 0.822 0.854 -0.241 0.666 2.968
mu_bc_H[6] -2.184 0.325 -2.815 -2.186 -1.536
mu_bc_H[7] -0.460 0.109 -0.680 -0.454 -0.260
mu_bc_H[8] 0.215 0.339 -0.370 0.181 0.965
mu_bc_H[9] -0.290 0.132 -0.548 -0.291 -0.017
mu_bc_H[10] -0.110 0.071 -0.249 -0.112 0.030
mu_bc_H[11] -0.125 0.040 -0.206 -0.124 -0.050
mu_bc_H[12] -0.266 0.107 -0.495 -0.258 -0.070
mu_bc_H[13] -0.150 0.087 -0.329 -0.149 0.020
mu_bc_H[14] -0.316 0.104 -0.541 -0.312 -0.122
mu_bc_H[15] -0.350 0.052 -0.454 -0.352 -0.245
mu_bc_H[16] -0.359 0.406 -1.102 -0.377 0.530
mu_bc_R[1] 1.334 0.147 1.055 1.333 1.628
mu_bc_R[2] 1.465 0.094 1.283 1.465 1.649
mu_bc_R[3] 1.396 0.142 1.110 1.397 1.663
mu_bc_R[4] 0.942 0.207 0.530 0.950 1.322
mu_bc_R[5] 1.283 0.481 0.343 1.287 2.230
mu_bc_R[6] -1.509 0.468 -2.384 -1.523 -0.534
mu_bc_R[7] 0.436 0.200 0.029 0.438 0.813
mu_bc_R[8] 0.544 0.190 0.160 0.543 0.914
mu_bc_R[9] 0.366 0.202 -0.064 0.379 0.724
mu_bc_R[10] 1.329 0.171 1.002 1.332 1.659
mu_bc_R[11] 1.048 0.103 0.854 1.046 1.250
mu_bc_R[12] 0.829 0.203 0.421 0.832 1.226
mu_bc_R[13] 1.043 0.107 0.827 1.042 1.265
mu_bc_R[14] 0.911 0.146 0.622 0.911 1.195
mu_bc_R[15] 0.794 0.120 0.557 0.793 1.029
mu_bc_R[16] 1.107 0.137 0.842 1.107 1.375
tau_pH[1] 4.205 1.760 0.202 4.927 5.944
tau_pH[2] 1.965 0.224 1.570 1.952 2.433
tau_pH[3] 2.148 0.217 1.760 2.139 2.592
beta0_pH[1,1] 0.766 0.552 0.207 0.596 2.439
beta0_pH[2,1] 1.574 1.283 -0.261 1.398 5.442
beta0_pH[3,1] 1.597 0.521 0.992 1.482 3.280
beta0_pH[4,1] 1.776 0.498 1.155 1.652 3.168
beta0_pH[5,1] -0.505 0.723 -1.343 -0.716 1.508
beta0_pH[6,1] -0.806 1.587 -6.906 -0.523 0.962
beta0_pH[7,1] 0.153 0.589 -0.778 0.015 1.444
beta0_pH[8,1] -0.460 0.537 -1.182 -0.570 0.993
beta0_pH[9,1] -0.355 0.602 -1.146 -0.511 1.074
beta0_pH[10,1] 0.613 0.678 -0.334 0.462 2.895
beta0_pH[11,1] 0.687 1.857 -0.503 -0.048 6.561
beta0_pH[12,1] 0.728 0.607 0.107 0.544 2.513
beta0_pH[13,1] 0.516 1.228 -0.263 0.048 4.768
beta0_pH[14,1] 0.007 0.759 -0.620 -0.262 2.143
beta0_pH[15,1] 0.455 1.106 -0.341 0.055 4.265
beta0_pH[16,1] 0.118 1.185 -1.147 -0.302 3.284
beta0_pH[1,2] 2.833 0.164 2.504 2.836 3.140
beta0_pH[2,2] 2.884 0.136 2.604 2.888 3.146
beta0_pH[3,2] 3.130 0.153 2.842 3.124 3.450
beta0_pH[4,2] 2.951 0.133 2.698 2.952 3.218
beta0_pH[5,2] 4.774 1.377 3.003 4.500 8.454
beta0_pH[6,2] 3.113 0.211 2.706 3.113 3.524
beta0_pH[7,2] 1.837 0.199 1.449 1.840 2.220
beta0_pH[8,2] 2.871 0.177 2.525 2.872 3.205
beta0_pH[9,2] 3.440 0.221 3.003 3.437 3.887
beta0_pH[10,2] 3.698 0.208 3.308 3.696 4.105
beta0_pH[11,2] -4.894 0.310 -5.479 -4.892 -4.256
beta0_pH[12,2] -4.772 0.370 -5.490 -4.773 -4.022
beta0_pH[13,2] -4.591 0.388 -5.325 -4.604 -3.792
beta0_pH[14,2] -5.576 0.474 -6.503 -5.540 -4.763
beta0_pH[15,2] -4.299 0.352 -4.965 -4.295 -3.571
beta0_pH[16,2] -4.852 0.400 -5.683 -4.856 -4.057
beta0_pH[1,3] -0.155 0.763 -1.959 -0.032 1.014
beta0_pH[2,3] 2.191 0.157 1.888 2.192 2.490
beta0_pH[3,3] 2.530 0.151 2.236 2.532 2.818
beta0_pH[4,3] 2.969 0.159 2.648 2.969 3.280
beta0_pH[5,3] 1.993 1.321 0.376 1.705 5.333
beta0_pH[6,3] 0.973 0.490 -0.212 1.002 1.829
beta0_pH[7,3] 0.632 0.169 0.308 0.628 0.962
beta0_pH[8,3] 0.306 0.188 -0.073 0.310 0.671
beta0_pH[9,3] -0.632 0.398 -1.641 -0.590 0.032
beta0_pH[10,3] 0.442 0.428 -0.662 0.515 1.086
beta0_pH[11,3] -0.230 0.318 -0.825 -0.240 0.434
beta0_pH[12,3] -0.856 0.346 -1.600 -0.829 -0.264
beta0_pH[13,3] -0.160 0.347 -0.903 -0.139 0.470
beta0_pH[14,3] -0.305 0.265 -0.815 -0.304 0.229
beta0_pH[15,3] -0.773 0.343 -1.552 -0.782 -0.126
beta0_pH[16,3] -0.388 0.301 -0.964 -0.390 0.246
beta1_pH[1,1] 2.755 0.875 0.001 2.998 3.764
beta1_pH[2,1] 2.274 1.062 0.003 2.144 5.381
beta1_pH[3,1] 1.743 0.691 0.001 1.884 2.870
beta1_pH[4,1] 2.115 0.807 0.001 2.276 3.335
beta1_pH[5,1] 1.921 0.765 0.000 2.116 2.874
beta1_pH[6,1] 3.747 3.368 0.000 3.198 17.280
beta1_pH[7,1] 1.397 0.935 0.000 1.330 3.045
beta1_pH[8,1] 3.294 1.601 0.000 3.436 6.252
beta1_pH[9,1] 1.931 0.812 0.000 2.128 3.043
beta1_pH[10,1] 1.915 0.813 0.000 2.065 3.270
beta1_pH[11,1] 2.794 1.127 0.000 3.222 3.798
beta1_pH[12,1] 2.230 0.803 0.000 2.490 2.963
beta1_pH[13,1] 2.556 0.992 0.000 2.913 3.424
beta1_pH[14,1] 2.990 1.043 0.000 3.348 3.843
beta1_pH[15,1] 2.134 0.828 0.000 2.428 2.898
beta1_pH[16,1] 3.380 1.519 0.000 3.855 5.232
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,2] 0.000 0.000 0.000 0.000 0.001
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.715 0.346 6.033 6.732 7.373
beta1_pH[12,2] 6.426 0.423 5.596 6.427 7.250
beta1_pH[13,2] 6.959 0.426 6.110 6.958 7.785
beta1_pH[14,2] 7.205 0.494 6.341 7.172 8.198
beta1_pH[15,2] 6.765 0.381 5.996 6.773 7.489
beta1_pH[16,2] 7.434 0.443 6.581 7.433 8.341
beta1_pH[1,3] 4.639 1.649 2.178 4.311 8.202
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.351 3.863 0.925 2.746 8.873
beta1_pH[6,3] 2.926 2.270 0.471 2.626 7.528
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.755 0.347 2.074 2.750 3.451
beta1_pH[9,3] 2.756 0.462 1.978 2.719 3.911
beta1_pH[10,3] 2.935 0.510 2.154 2.859 4.214
beta1_pH[11,3] 2.810 0.379 2.058 2.812 3.564
beta1_pH[12,3] 4.113 0.436 3.327 4.089 5.023
beta1_pH[13,3] 1.728 0.358 1.043 1.727 2.468
beta1_pH[14,3] 2.567 0.340 1.899 2.565 3.246
beta1_pH[15,3] 2.033 0.369 1.281 2.035 2.829
beta1_pH[16,3] 1.781 0.326 1.114 1.792 2.402
beta2_pH[1,1] 1.706 3.678 0.286 0.491 14.101
beta2_pH[2,1] 1.742 3.738 0.066 0.537 14.599
beta2_pH[3,1] 1.892 3.682 0.170 0.618 14.723
beta2_pH[4,1] 1.663 3.684 0.184 0.472 14.324
beta2_pH[5,1] 1.572 1.544 -1.417 1.512 4.622
beta2_pH[6,1] 0.266 1.092 -1.213 0.183 2.682
beta2_pH[7,1] 1.936 3.054 0.000 0.013 9.697
beta2_pH[8,1] 0.361 1.107 -1.595 0.241 2.738
beta2_pH[9,1] 0.558 1.066 -0.999 0.427 2.950
beta2_pH[10,1] 0.674 1.167 -1.083 0.587 3.203
beta2_pH[11,1] 0.814 1.548 -1.709 0.718 4.557
beta2_pH[12,1] 1.275 1.552 -1.830 1.181 4.269
beta2_pH[13,1] 0.836 1.491 -1.608 0.696 4.521
beta2_pH[14,1] 0.918 1.522 -1.676 0.805 4.612
beta2_pH[15,1] 1.030 1.577 -0.112 0.803 5.090
beta2_pH[16,1] 0.273 1.550 -4.013 0.320 3.727
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -1.980 1.831 -6.588 -1.498 -0.027
beta2_pH[4,2] -1.990 1.829 -6.979 -1.524 -0.029
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.309 4.274 -20.035 -8.328 -3.870
beta2_pH[12,2] -7.898 4.914 -20.013 -6.986 -1.126
beta2_pH[13,2] -7.769 4.794 -20.102 -6.721 -1.685
beta2_pH[14,2] -8.478 4.626 -20.101 -7.378 -2.634
beta2_pH[15,2] -9.217 4.363 -20.147 -8.157 -3.595
beta2_pH[16,2] -9.444 4.286 -20.075 -8.426 -3.975
beta2_pH[1,3] 0.237 0.250 0.101 0.184 0.630
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 8.979 6.455 -0.193 8.116 23.768
beta2_pH[6,3] 9.132 6.389 0.164 8.088 24.057
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 10.004 5.844 1.837 8.831 23.945
beta2_pH[9,3] 8.996 6.383 0.475 7.933 23.779
beta2_pH[10,3] 8.552 6.680 0.449 7.522 24.107
beta2_pH[11,3] -2.213 2.030 -8.050 -1.608 -0.593
beta2_pH[12,3] -2.355 1.836 -7.622 -1.834 -0.937
beta2_pH[13,3] -2.773 2.310 -9.360 -2.061 -0.651
beta2_pH[14,3] -2.760 2.144 -8.849 -2.085 -0.836
beta2_pH[15,3] -2.860 2.228 -9.485 -2.145 -0.827
beta2_pH[16,3] -2.936 2.360 -9.928 -2.166 -0.845
beta3_pH[1,1] 35.791 2.658 26.536 35.967 40.918
beta3_pH[2,1] 32.650 4.617 19.974 33.443 41.191
beta3_pH[3,1] 33.126 2.903 23.315 33.527 37.066
beta3_pH[4,1] 33.415 3.259 22.350 33.836 37.688
beta3_pH[5,1] 28.119 3.218 21.965 27.472 38.518
beta3_pH[6,1] 36.825 4.915 22.540 37.140 44.766
beta3_pH[7,1] 32.321 8.519 18.713 31.781 45.630
beta3_pH[8,1] 37.598 5.261 21.722 38.730 44.543
beta3_pH[9,1] 30.945 3.495 23.588 30.621 42.071
beta3_pH[10,1] 32.294 3.636 20.503 32.859 38.435
beta3_pH[11,1] 31.829 3.994 29.342 30.434 44.792
beta3_pH[12,1] 30.699 1.994 29.304 30.222 37.352
beta3_pH[13,1] 34.302 3.064 31.947 33.292 44.071
beta3_pH[14,1] 32.617 2.169 31.004 32.108 40.857
beta3_pH[15,1] 31.656 1.365 29.878 31.410 35.776
beta3_pH[16,1] 33.105 3.158 30.097 32.237 43.762
beta3_pH[1,2] 30.214 7.979 18.455 29.301 44.887
beta3_pH[2,2] 29.845 7.988 18.463 28.920 44.918
beta3_pH[3,2] 30.115 8.012 18.496 29.194 44.874
beta3_pH[4,2] 29.985 7.961 18.446 29.013 44.923
beta3_pH[5,2] 30.069 7.950 18.460 29.054 44.790
beta3_pH[6,2] 30.019 7.965 18.429 28.926 45.036
beta3_pH[7,2] 30.072 8.091 18.530 29.132 44.984
beta3_pH[8,2] 29.989 7.848 18.480 28.753 44.798
beta3_pH[9,2] 29.896 7.987 18.513 28.812 44.722
beta3_pH[10,2] 30.146 7.929 18.432 29.230 44.949
beta3_pH[11,2] 43.407 0.185 43.112 43.385 43.783
beta3_pH[12,2] 43.188 0.192 42.919 43.145 43.709
beta3_pH[13,2] 43.869 0.148 43.453 43.909 44.046
beta3_pH[14,2] 43.303 0.202 43.046 43.250 43.797
beta3_pH[15,2] 43.413 0.197 43.104 43.386 43.821
beta3_pH[16,2] 43.494 0.189 43.158 43.491 43.848
beta3_pH[1,3] 38.944 3.324 32.436 38.834 45.224
beta3_pH[2,3] 30.155 7.971 18.461 29.201 45.125
beta3_pH[3,3] 30.141 7.912 18.496 29.283 44.881
beta3_pH[4,3] 30.215 7.990 18.422 29.459 44.923
beta3_pH[5,3] 36.732 3.900 31.208 36.209 45.077
beta3_pH[6,3] 40.358 3.529 31.820 40.774 45.566
beta3_pH[7,3] 37.866 4.255 31.291 37.559 45.490
beta3_pH[8,3] 41.497 0.247 41.056 41.494 41.936
beta3_pH[9,3] 33.469 0.591 31.563 33.571 34.275
beta3_pH[10,3] 35.781 0.877 33.296 36.013 36.863
beta3_pH[11,3] 41.888 0.723 40.427 41.894 43.251
beta3_pH[12,3] 41.744 0.391 40.972 41.765 42.534
beta3_pH[13,3] 42.808 1.009 40.989 42.791 45.299
beta3_pH[14,3] 41.097 0.566 39.858 41.138 42.101
beta3_pH[15,3] 42.723 0.676 41.355 42.814 43.886
beta3_pH[16,3] 42.896 0.762 41.174 42.998 44.195
beta0_pelagic[1] 2.223 0.133 1.965 2.222 2.486
beta0_pelagic[2] 1.511 0.131 1.274 1.504 1.798
beta0_pelagic[3] -0.132 0.612 -1.706 0.027 0.616
beta0_pelagic[4] -0.078 0.599 -1.441 0.022 0.850
beta0_pelagic[5] 1.198 0.251 0.680 1.206 1.678
beta0_pelagic[6] 1.465 0.266 0.885 1.479 1.951
beta0_pelagic[7] 1.602 0.214 1.205 1.595 2.064
beta0_pelagic[8] 1.756 0.207 1.332 1.757 2.174
beta0_pelagic[9] 2.466 0.314 1.845 2.463 3.062
beta0_pelagic[10] 2.500 0.201 2.057 2.514 2.858
beta0_pelagic[11] -0.482 0.477 -1.439 -0.471 0.442
beta0_pelagic[12] 1.675 0.146 1.386 1.678 1.960
beta0_pelagic[13] 0.296 0.174 -0.064 0.307 0.613
beta0_pelagic[14] -0.188 0.244 -0.723 -0.170 0.254
beta0_pelagic[15] -0.317 0.142 -0.592 -0.325 -0.034
beta0_pelagic[16] -0.102 0.297 -0.801 -0.053 0.365
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.595 1.108 0.436 1.314 4.883
beta1_pelagic[4] 1.364 0.611 0.402 1.243 2.672
beta1_pelagic[5] -0.082 0.306 -0.674 -0.076 0.503
beta1_pelagic[6] -0.101 0.452 -0.870 -0.153 0.749
beta1_pelagic[7] -0.036 0.292 -0.594 -0.040 0.547
beta1_pelagic[8] -0.003 0.283 -0.544 -0.006 0.556
beta1_pelagic[9] 0.217 0.485 -0.788 0.340 0.961
beta1_pelagic[10] 0.065 0.277 -0.465 0.060 0.642
beta1_pelagic[11] 4.382 1.111 2.633 4.200 6.710
beta1_pelagic[12] 2.866 0.407 2.204 2.823 3.853
beta1_pelagic[13] 3.126 0.867 1.798 2.997 4.979
beta1_pelagic[14] 4.753 1.076 3.147 4.603 7.263
beta1_pelagic[15] 2.973 0.259 2.414 2.971 3.434
beta1_pelagic[16] 4.979 1.124 3.237 4.896 7.543
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.934 2.633 0.032 0.208 9.648
beta2_pelagic[4] 1.202 2.805 0.084 0.382 9.947
beta2_pelagic[5] -0.016 0.670 -1.399 -0.012 1.375
beta2_pelagic[6] -0.100 0.673 -1.460 -0.143 1.300
beta2_pelagic[7] 0.005 0.659 -1.378 0.015 1.427
beta2_pelagic[8] 0.002 0.644 -1.368 -0.003 1.345
beta2_pelagic[9] 0.212 0.672 -1.179 0.263 1.566
beta2_pelagic[10] -0.167 0.641 -1.807 -0.078 1.002
beta2_pelagic[11] 0.282 0.751 0.103 0.167 1.640
beta2_pelagic[12] 3.565 2.925 0.586 2.772 11.726
beta2_pelagic[13] 0.554 0.598 0.197 0.396 1.872
beta2_pelagic[14] 0.272 0.081 0.161 0.258 0.468
beta2_pelagic[15] 3.559 2.877 0.752 2.714 11.393
beta2_pelagic[16] 0.537 1.489 0.155 0.279 3.553
beta3_pelagic[1] 29.837 7.766 18.527 28.906 44.469
beta3_pelagic[2] 30.083 7.922 18.503 29.208 44.936
beta3_pelagic[3] 30.805 5.708 20.868 30.201 43.908
beta3_pelagic[4] 24.938 3.997 19.121 24.551 36.639
beta3_pelagic[5] 30.220 8.221 18.554 28.800 45.246
beta3_pelagic[6] 31.752 6.655 18.942 31.703 44.111
beta3_pelagic[7] 29.602 7.878 18.449 28.578 44.875
beta3_pelagic[8] 29.136 7.841 18.404 27.598 44.822
beta3_pelagic[9] 30.549 6.067 19.149 30.420 42.578
beta3_pelagic[10] 29.166 8.056 18.393 27.680 44.845
beta3_pelagic[11] 40.407 3.478 32.769 40.969 45.582
beta3_pelagic[12] 43.513 0.381 42.937 43.474 44.467
beta3_pelagic[13] 43.016 1.500 40.328 43.001 45.772
beta3_pelagic[14] 42.629 1.808 39.153 42.555 45.817
beta3_pelagic[15] 43.000 0.354 42.143 43.075 43.527
beta3_pelagic[16] 43.088 1.489 40.026 43.123 45.697
mu_beta0_pelagic[1] 0.808 0.995 -1.404 0.878 2.624
mu_beta0_pelagic[2] 1.811 0.384 1.018 1.807 2.611
mu_beta0_pelagic[3] 0.135 0.524 -0.930 0.146 1.126
tau_beta0_pelagic[1] 0.606 0.682 0.053 0.372 2.506
tau_beta0_pelagic[2] 2.810 2.856 0.232 2.056 10.047
tau_beta0_pelagic[3] 1.233 0.959 0.151 1.007 3.747
beta0_yellow[1] -0.536 0.201 -1.019 -0.514 -0.215
beta0_yellow[2] 0.466 0.193 0.023 0.484 0.764
beta0_yellow[3] -0.322 0.175 -0.666 -0.319 0.009
beta0_yellow[4] 0.847 0.267 0.135 0.894 1.217
beta0_yellow[5] -0.294 0.352 -0.988 -0.290 0.391
beta0_yellow[6] 1.112 0.168 0.785 1.110 1.444
beta0_yellow[7] 0.986 0.163 0.671 0.984 1.311
beta0_yellow[8] 1.012 0.154 0.706 1.012 1.303
beta0_yellow[9] 0.661 0.162 0.337 0.659 0.980
beta0_yellow[10] 0.588 0.141 0.311 0.587 0.869
beta0_yellow[11] -2.012 0.448 -2.851 -2.039 -1.126
beta0_yellow[12] -3.680 0.386 -4.429 -3.687 -2.917
beta0_yellow[13] -3.663 0.508 -4.689 -3.621 -2.726
beta0_yellow[14] -2.160 0.603 -3.218 -2.190 -0.930
beta0_yellow[15] -2.935 0.494 -4.051 -2.918 -2.114
beta0_yellow[16] -2.429 0.543 -3.530 -2.409 -1.441
beta1_yellow[1] 2.703 6.642 0.011 0.715 27.064
beta1_yellow[2] 1.152 0.561 0.593 1.047 2.857
beta1_yellow[3] 0.714 0.298 0.248 0.705 1.221
beta1_yellow[4] 1.404 0.804 0.650 1.173 4.016
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 2.177 0.459 1.335 2.201 3.092
beta1_yellow[12] 2.479 0.382 1.668 2.497 3.220
beta1_yellow[13] 2.786 0.504 1.817 2.750 3.825
beta1_yellow[14] 2.287 0.568 1.126 2.295 3.356
beta1_yellow[15] 2.178 0.498 1.339 2.149 3.269
beta1_yellow[16] 2.181 0.540 1.220 2.136 3.262
beta2_yellow[1] -3.440 3.004 -11.131 -2.701 -0.061
beta2_yellow[2] -2.932 2.744 -10.120 -2.108 -0.126
beta2_yellow[3] -3.293 2.842 -10.593 -2.510 -0.154
beta2_yellow[4] -2.756 2.818 -9.645 -1.811 -0.097
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -4.313 2.642 -11.451 -3.626 -1.112
beta2_yellow[12] -4.760 2.630 -11.653 -4.148 -1.418
beta2_yellow[13] -4.533 2.492 -11.170 -3.868 -1.505
beta2_yellow[14] -4.205 2.746 -11.181 -3.626 -0.119
beta2_yellow[15] -3.842 2.497 -10.365 -3.162 -0.904
beta2_yellow[16] -4.650 2.705 -11.645 -3.980 -1.325
beta3_yellow[1] 25.321 7.281 18.154 22.304 44.350
beta3_yellow[2] 28.935 2.138 22.420 28.956 32.571
beta3_yellow[3] 32.986 3.015 26.023 32.962 38.890
beta3_yellow[4] 28.770 3.574 20.450 27.959 35.992
beta3_yellow[5] 30.116 7.915 18.573 29.325 44.757
beta3_yellow[6] 30.024 7.913 18.484 28.896 44.806
beta3_yellow[7] 30.199 8.017 18.459 29.379 45.058
beta3_yellow[8] 29.948 7.921 18.419 28.953 44.734
beta3_yellow[9] 30.078 7.942 18.624 29.265 44.915
beta3_yellow[10] 29.999 8.028 18.397 29.007 44.901
beta3_yellow[11] 45.345 0.505 44.093 45.439 45.974
beta3_yellow[12] 43.291 0.367 42.563 43.273 43.986
beta3_yellow[13] 44.816 0.420 43.924 44.895 45.522
beta3_yellow[14] 43.891 2.161 34.883 44.278 45.827
beta3_yellow[15] 45.226 0.520 44.175 45.255 45.974
beta3_yellow[16] 44.603 0.658 43.387 44.593 45.850
mu_beta0_yellow[1] 0.095 0.539 -1.000 0.089 1.273
mu_beta0_yellow[2] 0.643 0.336 -0.108 0.663 1.270
mu_beta0_yellow[3] -2.458 0.669 -3.511 -2.555 -0.795
tau_beta0_yellow[1] 1.960 2.905 0.096 1.175 8.045
tau_beta0_yellow[2] 3.548 4.334 0.306 2.358 14.165
tau_beta0_yellow[3] 1.464 1.708 0.092 0.962 5.781
beta0_black[1] -0.081 0.163 -0.402 -0.082 0.238
beta0_black[2] 1.914 0.130 1.654 1.914 2.162
beta0_black[3] 1.318 0.139 1.039 1.318 1.589
beta0_black[4] 2.429 0.134 2.167 2.430 2.686
beta0_black[5] 4.645 2.113 1.885 4.194 10.167
beta0_black[6] 4.634 1.959 2.264 4.179 9.759
beta0_black[7] 3.767 1.841 1.621 3.282 8.759
beta0_black[8] 0.971 0.211 0.559 0.964 1.391
beta0_black[9] 2.605 0.237 2.139 2.603 3.093
beta0_black[10] 1.460 0.135 1.196 1.461 1.730
beta0_black[11] 3.483 0.154 3.181 3.485 3.784
beta0_black[12] 4.865 0.175 4.517 4.868 5.200
beta0_black[13] -0.139 0.242 -0.614 -0.128 0.307
beta0_black[14] 2.854 0.161 2.544 2.854 3.165
beta0_black[15] 1.294 0.159 0.986 1.292 1.614
beta0_black[16] 4.275 0.161 3.958 4.275 4.593
beta2_black[1] 7.907 10.253 0.481 3.428 40.472
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.850 1.540 -6.135 -1.351 -0.347
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.788 1.206 39.903 41.929 43.590
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.223 0.879 37.207 39.319 40.619
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.256 0.193 -0.631 -0.259 0.115
beta4_black[2] 0.237 0.187 -0.123 0.240 0.609
beta4_black[3] -0.933 0.202 -1.322 -0.938 -0.540
beta4_black[4] 0.422 0.214 -0.002 0.422 0.828
beta4_black[5] 0.544 1.337 -1.396 0.322 3.661
beta4_black[6] 0.553 1.331 -1.311 0.325 3.797
beta4_black[7] 0.448 1.236 -1.371 0.279 3.347
beta4_black[8] -0.255 0.316 -0.892 -0.250 0.346
beta4_black[9] 0.869 0.806 -0.237 0.697 2.981
beta4_black[10] 0.052 0.184 -0.308 0.053 0.415
beta4_black[11] -0.694 0.217 -1.108 -0.698 -0.267
beta4_black[12] 0.172 0.328 -0.451 0.166 0.831
beta4_black[13] -1.187 0.228 -1.626 -1.186 -0.743
beta4_black[14] -0.180 0.244 -0.641 -0.185 0.303
beta4_black[15] -0.886 0.216 -1.310 -0.879 -0.473
beta4_black[16] -0.593 0.229 -1.050 -0.593 -0.141
mu_beta0_black[1] 1.290 0.914 -0.743 1.346 3.131
mu_beta0_black[2] 2.746 1.070 0.797 2.637 5.254
mu_beta0_black[3] 2.509 0.986 0.357 2.532 4.422
tau_beta0_black[1] 0.633 0.581 0.054 0.453 2.195
tau_beta0_black[2] 0.454 0.598 0.047 0.243 2.185
tau_beta0_black[3] 0.240 0.163 0.051 0.200 0.667
beta0_dsr[11] -2.918 0.382 -3.713 -2.884 -2.297
beta0_dsr[12] 4.562 0.284 4.018 4.558 5.138
beta0_dsr[13] -1.477 0.568 -3.453 -1.377 -0.800
beta0_dsr[14] -3.718 0.490 -4.799 -3.701 -2.798
beta0_dsr[15] -2.253 1.001 -5.523 -1.992 -1.428
beta0_dsr[16] -2.995 0.362 -3.705 -2.992 -2.298
beta1_dsr[11] 4.906 0.614 4.236 4.833 6.004
beta1_dsr[12] 6.805 8.832 2.247 5.159 22.333
beta1_dsr[13] 3.034 0.761 2.276 2.890 5.845
beta1_dsr[14] 6.385 0.520 5.396 6.370 7.487
beta1_dsr[15] 3.840 1.721 2.786 3.389 10.888
beta1_dsr[16] 5.817 0.377 5.096 5.812 6.551
beta2_dsr[11] -8.307 2.940 -14.396 -8.047 -0.646
beta2_dsr[12] -7.067 2.869 -13.116 -6.929 -1.927
beta2_dsr[13] -6.305 3.280 -13.000 -6.273 -0.239
beta2_dsr[14] -6.358 2.952 -12.606 -6.269 -1.666
beta2_dsr[15] -7.264 3.342 -13.544 -7.412 -0.082
beta2_dsr[16] -8.027 2.429 -13.702 -7.754 -4.162
beta3_dsr[11] 43.465 0.295 43.158 43.485 43.796
beta3_dsr[12] 33.929 0.754 31.997 34.109 34.809
beta3_dsr[13] 43.311 0.437 42.765 43.204 44.527
beta3_dsr[14] 43.338 0.231 43.074 43.267 43.891
beta3_dsr[15] 43.554 0.891 43.105 43.522 45.600
beta3_dsr[16] 43.438 0.158 43.172 43.427 43.763
beta4_dsr[11] 0.577 0.217 0.164 0.575 1.009
beta4_dsr[12] 0.250 0.441 -0.629 0.245 1.120
beta4_dsr[13] -0.158 0.214 -0.578 -0.152 0.258
beta4_dsr[14] 0.151 0.248 -0.333 0.154 0.649
beta4_dsr[15] 0.720 0.217 0.294 0.715 1.151
beta4_dsr[16] 0.147 0.233 -0.316 0.152 0.591
beta0_slope[11] -1.838 0.145 -2.126 -1.836 -1.552
beta0_slope[12] -4.479 0.259 -5.013 -4.471 -4.005
beta0_slope[13] -1.347 0.185 -1.770 -1.337 -1.034
beta0_slope[14] -2.673 0.164 -2.985 -2.675 -2.354
beta0_slope[15] -1.343 0.149 -1.639 -1.342 -1.053
beta0_slope[16] -2.729 0.158 -3.026 -2.732 -2.415
beta1_slope[11] 4.483 0.219 4.060 4.487 4.911
beta1_slope[12] 3.992 0.456 3.088 3.991 4.881
beta1_slope[13] 2.762 0.538 2.190 2.653 4.623
beta1_slope[14] 6.329 0.419 5.521 6.322 7.168
beta1_slope[15] 3.010 0.207 2.604 3.010 3.421
beta1_slope[16] 5.274 0.286 4.735 5.267 5.862
beta2_slope[11] 8.630 2.283 5.120 8.270 13.952
beta2_slope[12] 6.573 2.964 1.162 6.606 12.696
beta2_slope[13] 5.241 3.144 0.328 5.178 11.866
beta2_slope[14] 6.308 2.413 2.244 6.237 11.389
beta2_slope[15] 8.101 2.451 4.345 7.727 13.731
beta2_slope[16] 7.716 2.251 4.141 7.420 12.987
beta3_slope[11] 43.462 0.133 43.225 43.458 43.725
beta3_slope[12] 43.355 0.280 42.905 43.317 43.904
beta3_slope[13] 43.481 0.439 42.898 43.408 44.557
beta3_slope[14] 43.267 0.134 43.098 43.235 43.601
beta3_slope[15] 43.492 0.159 43.196 43.493 43.796
beta3_slope[16] 43.373 0.145 43.150 43.355 43.694
beta4_slope[11] -0.735 0.161 -1.054 -0.737 -0.418
beta4_slope[12] -1.157 0.461 -2.146 -1.126 -0.369
beta4_slope[13] 0.082 0.165 -0.245 0.079 0.403
beta4_slope[14] -0.085 0.195 -0.468 -0.088 0.289
beta4_slope[15] -0.764 0.160 -1.087 -0.762 -0.456
beta4_slope[16] -0.164 0.174 -0.503 -0.165 0.183
sigma_H[1] 0.198 0.053 0.105 0.195 0.311
sigma_H[2] 0.172 0.029 0.122 0.170 0.235
sigma_H[3] 0.195 0.042 0.120 0.193 0.283
sigma_H[4] 0.417 0.078 0.293 0.408 0.597
sigma_H[5] 0.988 0.210 0.612 0.981 1.416
sigma_H[6] 0.421 0.197 0.050 0.416 0.810
sigma_H[7] 0.309 0.064 0.210 0.300 0.462
sigma_H[8] 0.418 0.096 0.275 0.407 0.623
sigma_H[9] 0.517 0.130 0.322 0.497 0.814
sigma_H[10] 0.213 0.043 0.142 0.210 0.309
sigma_H[11] 0.279 0.046 0.200 0.275 0.380
sigma_H[12] 0.435 0.168 0.203 0.409 0.777
sigma_H[13] 0.212 0.038 0.147 0.208 0.295
sigma_H[14] 0.501 0.095 0.339 0.496 0.702
sigma_H[15] 0.245 0.040 0.181 0.241 0.336
sigma_H[16] 0.230 0.045 0.156 0.225 0.332
lambda_H[1] 3.216 5.630 0.152 1.822 13.334
lambda_H[2] 8.546 7.963 0.766 6.213 29.271
lambda_H[3] 6.388 9.493 0.300 3.263 32.134
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.125 6.369 0.029 0.861 21.643
lambda_H[6] 5.939 12.741 0.008 0.521 40.847
lambda_H[7] 0.013 0.009 0.002 0.011 0.037
lambda_H[8] 8.135 10.464 0.003 4.416 37.869
lambda_H[9] 0.016 0.011 0.003 0.013 0.043
lambda_H[10] 0.314 0.724 0.031 0.197 1.122
lambda_H[11] 0.309 0.522 0.012 0.157 1.514
lambda_H[12] 4.990 6.496 0.221 2.965 21.549
lambda_H[13] 3.711 3.439 0.266 2.756 12.992
lambda_H[14] 3.439 4.285 0.233 2.107 14.688
lambda_H[15] 0.030 0.195 0.004 0.017 0.100
lambda_H[16] 1.491 2.423 0.058 0.651 8.190
mu_lambda_H[1] 4.395 1.915 1.288 4.183 8.580
mu_lambda_H[2] 3.713 1.913 0.546 3.568 7.776
mu_lambda_H[3] 3.613 1.878 0.746 3.355 7.899
sigma_lambda_H[1] 8.668 4.308 2.217 8.004 18.467
sigma_lambda_H[2] 8.182 4.630 0.894 7.637 18.349
sigma_lambda_H[3] 6.371 3.987 1.057 5.461 16.434
beta_H[1,1] 6.882 1.085 4.214 7.054 8.476
beta_H[2,1] 9.868 0.485 8.818 9.900 10.773
beta_H[3,1] 8.000 0.758 6.225 8.080 9.288
beta_H[4,1] 9.414 7.720 -6.116 9.651 23.892
beta_H[5,1] 0.070 2.430 -4.862 0.257 4.276
beta_H[6,1] 2.960 4.028 -7.117 4.433 7.743
beta_H[7,1] 0.426 5.854 -12.277 0.996 10.681
beta_H[8,1] 2.163 7.081 -2.393 1.299 23.139
beta_H[9,1] 13.166 5.576 2.249 13.100 24.537
beta_H[10,1] 7.059 1.747 3.285 7.158 10.310
beta_H[11,1] 5.405 3.393 -2.829 6.274 9.939
beta_H[12,1] 2.610 1.008 0.845 2.549 4.788
beta_H[13,1] 9.052 0.900 7.201 9.128 10.446
beta_H[14,1] 2.174 0.986 0.167 2.200 4.072
beta_H[15,1] -6.077 3.803 -12.916 -6.309 2.086
beta_H[16,1] 3.327 2.268 -0.561 3.190 8.456
beta_H[1,2] 7.902 0.248 7.390 7.906 8.365
beta_H[2,2] 10.025 0.136 9.749 10.025 10.297
beta_H[3,2] 8.944 0.195 8.552 8.944 9.325
beta_H[4,2] 3.551 1.468 0.808 3.455 6.685
beta_H[5,2] 1.945 0.994 -0.006 1.975 3.814
beta_H[6,2] 5.738 1.057 3.207 5.907 7.447
beta_H[7,2] 2.681 1.128 0.695 2.608 5.090
beta_H[8,2] 2.810 1.775 -2.965 3.127 4.188
beta_H[9,2] 3.415 1.104 1.335 3.385 5.690
beta_H[10,2] 8.202 0.354 7.482 8.212 8.879
beta_H[11,2] 9.704 0.617 8.819 9.578 11.167
beta_H[12,2] 3.951 0.359 3.270 3.937 4.674
beta_H[13,2] 9.133 0.254 8.669 9.124 9.643
beta_H[14,2] 4.027 0.356 3.367 4.022 4.743
beta_H[15,2] 11.360 0.688 9.902 11.390 12.640
beta_H[16,2] 4.736 0.882 3.111 4.703 6.526
beta_H[1,3] 8.473 0.242 8.031 8.467 8.986
beta_H[2,3] 10.079 0.121 9.835 10.079 10.322
beta_H[3,3] 9.617 0.161 9.306 9.615 9.953
beta_H[4,3] -2.464 0.895 -4.254 -2.446 -0.635
beta_H[5,3] 3.934 0.626 2.693 3.927 5.136
beta_H[6,3] 8.073 1.198 6.436 7.747 10.631
beta_H[7,3] -2.787 0.676 -4.110 -2.775 -1.477
beta_H[8,3] 5.377 0.836 4.668 5.220 8.118
beta_H[9,3] -2.749 0.798 -4.335 -2.759 -1.199
beta_H[10,3] 8.706 0.285 8.164 8.707 9.268
beta_H[11,3] 8.580 0.288 7.941 8.600 9.085
beta_H[12,3] 5.283 0.312 4.532 5.317 5.814
beta_H[13,3] 8.877 0.198 8.489 8.880 9.249
beta_H[14,3] 5.745 0.279 5.156 5.760 6.250
beta_H[15,3] 10.381 0.324 9.766 10.375 11.022
beta_H[16,3] 6.580 0.678 5.225 6.568 7.835
beta_H[1,4] 8.269 0.173 7.902 8.278 8.579
beta_H[2,4] 10.142 0.124 9.882 10.152 10.356
beta_H[3,4] 10.122 0.165 9.764 10.135 10.417
beta_H[4,4] 11.793 0.450 10.865 11.802 12.668
beta_H[5,4] 5.623 0.798 4.344 5.534 7.426
beta_H[6,4] 7.021 0.944 4.907 7.279 8.358
beta_H[7,4] 8.273 0.351 7.576 8.282 8.946
beta_H[8,4] 6.696 0.346 5.731 6.735 7.142
beta_H[9,4] 7.175 0.468 6.259 7.165 8.097
beta_H[10,4] 7.744 0.239 7.299 7.738 8.250
beta_H[11,4] 9.392 0.201 8.999 9.391 9.782
beta_H[12,4] 7.151 0.209 6.749 7.150 7.586
beta_H[13,4] 9.068 0.156 8.767 9.066 9.388
beta_H[14,4] 7.756 0.227 7.321 7.754 8.207
beta_H[15,4] 9.487 0.239 9.031 9.487 9.952
beta_H[16,4] 9.288 0.228 8.885 9.271 9.767
beta_H[1,5] 8.978 0.146 8.680 8.981 9.249
beta_H[2,5] 10.789 0.093 10.611 10.786 10.977
beta_H[3,5] 10.916 0.168 10.618 10.908 11.256
beta_H[4,5] 8.402 0.460 7.514 8.386 9.347
beta_H[5,5] 5.400 0.623 3.880 5.470 6.462
beta_H[6,5] 8.879 0.648 7.940 8.740 10.390
beta_H[7,5] 6.758 0.342 6.120 6.748 7.451
beta_H[8,5] 8.258 0.285 7.874 8.225 8.923
beta_H[9,5] 8.202 0.472 7.262 8.210 9.150
beta_H[10,5] 10.094 0.230 9.634 10.093 10.547
beta_H[11,5] 11.494 0.232 11.041 11.494 11.956
beta_H[12,5] 8.492 0.200 8.110 8.488 8.905
beta_H[13,5] 10.014 0.132 9.762 10.010 10.275
beta_H[14,5] 9.206 0.237 8.776 9.196 9.703
beta_H[15,5] 11.157 0.247 10.682 11.155 11.650
beta_H[16,5] 9.932 0.169 9.578 9.933 10.254
beta_H[1,6] 10.183 0.193 9.847 10.170 10.615
beta_H[2,6] 11.515 0.106 11.311 11.517 11.722
beta_H[3,6] 10.817 0.159 10.474 10.828 11.109
beta_H[4,6] 12.848 0.810 11.210 12.864 14.427
beta_H[5,6] 5.916 0.642 4.737 5.901 7.190
beta_H[6,6] 8.805 0.702 7.039 8.923 9.843
beta_H[7,6] 9.865 0.585 8.726 9.864 10.997
beta_H[8,6] 9.495 0.392 8.666 9.541 9.983
beta_H[9,6] 8.453 0.794 6.920 8.443 10.079
beta_H[10,6] 9.517 0.316 8.827 9.549 10.069
beta_H[11,6] 10.831 0.351 10.096 10.855 11.484
beta_H[12,6] 9.381 0.250 8.897 9.375 9.915
beta_H[13,6] 11.044 0.158 10.764 11.032 11.364
beta_H[14,6] 9.831 0.286 9.267 9.833 10.383
beta_H[15,6] 10.865 0.442 10.007 10.867 11.747
beta_H[16,6] 10.555 0.227 10.038 10.570 10.976
beta_H[1,7] 10.855 0.886 8.751 10.962 12.272
beta_H[2,7] 12.192 0.437 11.327 12.192 13.047
beta_H[3,7] 10.556 0.653 9.109 10.609 11.687
beta_H[4,7] 2.648 4.189 -5.243 2.495 11.341
beta_H[5,7] 6.506 1.959 2.958 6.406 11.159
beta_H[6,7] 9.643 2.634 4.491 9.575 16.614
beta_H[7,7] 10.531 2.928 4.794 10.524 16.389
beta_H[8,7] 11.129 1.588 9.419 10.950 14.784
beta_H[9,7] 4.414 4.069 -3.593 4.538 12.210
beta_H[10,7] 9.813 1.480 7.096 9.730 12.973
beta_H[11,7] 10.916 1.674 7.759 10.832 14.351
beta_H[12,7] 10.000 0.891 8.033 10.079 11.565
beta_H[13,7] 11.665 0.743 9.977 11.747 12.828
beta_H[14,7] 10.411 0.921 8.423 10.464 12.063
beta_H[15,7] 11.907 2.289 7.546 11.915 16.430
beta_H[16,7] 12.102 1.202 10.171 11.896 14.963
beta0_H[1] 8.655 12.585 -17.956 8.834 33.445
beta0_H[2] 10.609 6.490 -2.684 10.740 22.854
beta0_H[3] 9.769 9.250 -9.211 9.927 29.001
beta0_H[4] 6.737 183.598 -354.296 8.677 379.105
beta0_H[5] 4.219 27.895 -50.754 4.196 58.495
beta0_H[6] 7.813 46.898 -99.253 7.674 115.379
beta0_H[7] 3.728 135.367 -271.812 2.883 278.660
beta0_H[8] 6.939 59.471 -23.632 6.331 39.094
beta0_H[9] 8.688 121.053 -233.317 6.935 268.523
beta0_H[10] 8.690 34.220 -62.734 8.931 75.286
beta0_H[11] 8.506 44.618 -88.830 9.961 96.679
beta0_H[12] 6.996 10.633 -13.636 6.739 29.269
beta0_H[13] 9.987 11.107 -11.006 9.991 29.619
beta0_H[14] 7.280 11.528 -15.192 7.201 30.532
beta0_H[15] 4.138 109.309 -219.010 3.176 229.003
beta0_H[16] 7.901 20.680 -33.130 8.115 49.851